He said in his first few words "Due to NEXT being the only option via Apple". That means he is probably on a legacy plan.
OP, ATT will have a countdown page. Plug the normal phone purchase link into the address bar 2-3 minutes before the countdown timer expires:
http://www.att.com/shop/wireless/devices/smartphones.html
They will have already updated the website with the 6S and you will be able to place your order before the timer expires. Make sure youre already logged in ahead of time, and practice the ordering process with another phone so you can blow through it.
Done this for the 5 and 6 and worked like a charm, release day delivery with no website lag. My order is always placed 1-2 minutes before the actual go-live.